Answer:
56,161
Step-by-step Thought Process:
Use the equation: 
to solve this problem. Let x= time in years, a= initial amount, and r= growth rate.
= 
When you solve you get this number:
56,160.57516085
Round to the nearest whole number:
56,161
From 1st condition:
3^(x+1)=81
Take log on both sides,
➡ log [3^(x+1)]=log81
Use the property: log(x^a)=a logx
➡ (x+1) log 3=log(3⁴)
➡ (x+1) log 3=4×log 3
➡ (x+1)=4 (log 3 /log 3)
➡ x+1=4
➡ x=3➡↪➡↪ ANS
From 2nd condition, (Same process are repeated)
81^(x-y)=3
➡ 3^4(x-y)=3
➡ log [3^4(3-y)]=log 3
➡ 4(3-y) log 3=log 3
➡ (3-y)=(log 3)/(4log 3)
➡ 3-y=(1/4)
➡ y=11/4 ➡↪➡↪ ANS
Answer:
The distribution is 
Solution:
As per the question:
Total no. of riders = n
Now, suppose the 
is the time between the departure of the rider i - 1 and i from the cable car.
where
= independent exponential random variable whose rate is 
The general form is given by:
(a) Now, the time distribution of the last rider is given as the sum total of the time of each rider:
Now, the sum of the exponential random variable with with rate is given by:
